Iterative Schemes for Zero Points of Maximal Monotone Operators and Fixed Points of Nonexpansive Mappings and Their Applications

1School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea

Abstract

Two iterative schemes for finding a common element of the set of zero
points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the
sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are
obtained. Two strong convergence theorems are obtained which extend some previous work.
Moreover, the applications of the iterative schemes are demonstrated.